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UID:6435@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210426T140000
DTEND;TZID=Europe/Paris:20210426T150000
DTSTAMP:20241120T201431Z
URL:https://www.i2m.univ-amu.fr/evenements/infinite-dimensional-thurston-t
 heory-and-transcendental-dynamics-video-talk/
SUMMARY:Konstantin Bogdanov (I2M\, Aix-Marseille Université): Infinite-dim
 ensional Thurston theory and transcendental dynamics (video talk)
DESCRIPTION:Konstantin Bogdanov: \nIn complex dynamics it is often importan
 t to understand and describe the dynamical behavior of critical (or singul
 ar) orbits. For quadratic polynomials\, this leads to the study of the Man
 delbrot set and of its complement. In our talk we present a theorem which 
 classifies within certain families the transcendental entire functions for
  which all singular values escape\, that is\, inside of the complement of 
 the "transcendental analogue'' of the Mandelbrot set. A key to the proof o
 f the theorem is a generalization of the celebrated Thurston’s Topologic
 al Characterization of Rational Functions\, but for the case of infinite r
 ather than finite set of "punctures''. As in the classical theorem of Thur
 ston\, we consider a special "sigma-map'' acting on a Teichmüller space w
 hich is in our case infinite-dimensional.\n\nWe give a brief overview of t
 he project\, and afterwards we discuss some of the main ingredients using 
 the ``toy example'' of the exponential family.\n\nhttps://arxiv.org/abs/21
 02.00300\nhttps://arxiv.org/abs/2102.10728\nhttps://bbb1.cirm-math.fr/reco
 rding/f8939f316b2fcf15dc46838494c26d79d8de04ed-1619428635187.mp4\n\n\n\nLe
 cture room link: https://bbb1.cirm-math.fr/b/org-n9z-3je\n\n\n\nAccess c
 ode: 199176\n\n\n\n\n
CATEGORIES:Séminaire,Processus Déterminantaux (ERC IChaos),Virtual event
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